Transcript (mean). - cloudfront.net

Do 1 problem in which you do a
1-sample hypothesis test with
statistics (mean).
Veronica Coronado
Sandra Gomez
In the population, IQ scores are normally distributed
with a mean of 100. A charter school wants to know
if their students have an IQ that is higher than the
population mean.
They take a random sample of 15 students and
find that they have a mean IQ of 109 with a
standard deviation of 23
Ho: µ = 100
Ha: µ > 100
And our parameter is all the
students in the charter school.
Now we have to check our conditions to ensure they
meet limitations we are given.
1.Random sample and Independence
2.Normal
3.Big population
1.Random sample and Independence, can be
with or without replacement:
Each observation is collected randomly from
the population, and observations are
independent of each other. The sample can be
collected either with or without replacement
2. Normal Either the population
distribution is normal or the sample size is
large
3. Big population If the sample is collected
without replacement then the population
must be at least 10 times larger than the
sample size.
Mean
Hypothesis test
results:
μ : Mean of
population
H0 : μ = 100
HA : μ > 100
μ
Sample Mean
109
Std. Err.
5.9385745
DF
T-Stat
14
1.5155152
P-value
0.0759
Fail to reject the null hypothesis.
With an alpha level of 5% and pvalue about 7.5% there is not
sufficient evidence that all charter
school students have a higher IQ
than the population mean score.
According to the National Association of Colleges and
Employers, the average salary for a new college graduate
in 2013 was $45,327. A small academic program wants to
know if the average salary of their graduates is different
from $45,327. In a sample of 10 recent graduates, the
average starting salary was $48,000 with a
standard deviation of $8,700. Assume the annual starting
income for graduates of this program is approximately
normally distributed
Ho: µ= 45,327
Ha: µ≠ 45,327
And our parameter is the
average salary of all new
college graduates of 2013.
Now we have to check our conditions to ensure they
meet limitations we are given.
1. Random sample and Independence
2. Normal
3. Big population
Mean
Sample Mean
Std. Err.
DF
T-Stat
P-value
Hypothesis test results:
μ : Mean of population
H0 : μ = 45327
HA : μ ≠ 45327
μ
48000
2751.1816
9
0.97158255
0.3566
Fail to reject the null hypothesis. With the
alpha level 5% and a p-value about 35.6 %.
There is not sufficient evidence to suggest
the average salary of all new college
graduates is different from the average of
the National Association of Colleges and
Employers.
1. What is the letter used to represent sample?
2. Once we’ve used Stat Crunch to analyze our
data…what points must be made to justify a
complete answer?
3. What’s the difference between a one tailed and
a two tailed hypothesis?
4. Unless stated otherwise: what is the
normal “rejection zone”?
5. When would we reject or fail to
reject the null?
6. If there is no indicated “rejection
zone, what is the default that we use.